If now \(A\)  is arbitrary, there is in general no \(\mu ^A\in \mathcal {E}^+_A\)  having the property
\(\kappa \mu ^A=\kappa \mu \)  n.e. on \(A\) .Compare with Theorem REF (c). Nevertheless, a substantial theory of inner balayage of \(\mu \in \mathcal {E}^+\)  to arbitrary \(A\)  was developed [1]}, and this was performed by means of several alternative approaches described in Theorem REF  below.
